Taking Fractals off the Page
Fractals are one of the weirder things you may come across when studying computer science and programming algorithms. From Wikipedia: "A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between integers." This is a really odd concept—that you could have something like an image that isn't made up of lines or of surfaces, but something in between. The term fractal was coined by Benoit Mandelbrot in 1975.
A key property of fractals is that they are self-similar. This means if you zoom in on a fractal, it will look similar to the way the fractal looked originally. The concept of recursion also is very important here. Many types of fractal algorithms use recursion to generate the values in the given set. Almost everyone has seen computer generated images of classic fractals, like the Mandelbrot set or the Cantor set. One thing about all of these classic images is that they are two-dimensional (or actually greater than one and less than two-dimensional, if you want to be pedantic). But there is nothing that forces this to be the case. Fractals can be any dimension, including greater than two. And with modern 3-D graphics cards, there is no reason why you shouldn't be able to examine these and play with them. Now you can, with the software package Mandelbulber.
Mandelbulber is an experimental, open-source package that lets you render three-dimensional fractal images and interact with them. It is written using the GTK toolkit, so there are downloads available for Windows and Mac OS X as well as Linux. Actually, most Linux distributions should include it in their package management systems. If not, you always can download the source code and build it from scratch.
If you want some inspiration on what is possible with Mandelbulber, I strongly suggest you go check out the gallery of images that have been generated with this software. There are some truly innovative and amazing images out there, and some of them include the parameters you need in order to regenerate the image on your own. The Mandelbulber Wiki provides a large amount of information. When you are done reading this article, check out everything else that you can do with Mandelbulber.
When you first start up Mandelbulber, three windows open. The first is the parameters window (Figure 1). Along the very top are the two main buttons: render and stop. Below that is a list of 12 buttons that pull up different panes of parameters. You get an initial set of default parameters that will generate a 3-D version of the classic Mandelbrot set. Clicking on the render button will start the rendering process. If you have multiple cores on your machine, Mandelbulber will grab them to help speed up the calculations.
Figure 1. The main window gives you all parameters that control the generation of your fractal.
The rendered plot will be drawn in its own window (Figure 2). The third window shows you some measures of how the rendering progressed (Figure 3). You get two histograms describing the number of iterations and the number of steps.
Figure 2. This is what the default 3-D fractal looks like.
Figure 3. Histograms of the Rendering Progression
Joey Bernard has a background in both physics and computer science. This serves him well in his day job as a computational research consultant at the University of New Brunswick. He also teaches computational physics and parallel programming.
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